Successive Operations with a Real Variable Applied to the Representation of Special Functions and Computational Modeling (Doctoral Thesis Proposal)
This doctoral thesis proposal was prepared by Marlo Moesia in early 2024. It was defended and approved without restrictions by the examination committee appointed by LNCC on August 19, 2024. DOI: 10.29327/43427396.
ABSTRACT
Successive products were originally developed from successive operations applied to integer-indexed sequences and have since been used to solve recursive equations indexed by integers. This thesis extends successive products from the integer domain to the real domain by introducing a new recursive system of equations and establishing a methodology for solving it. The approach provides an efficient way to represent and compute familiar special functions, including the gamma function, factorials, and double factorials. It also enables the representation of other functions using successive products, offering a potential alternative for mathematical analysis and modeling.
Example of the application of the Successive Products Framework developed in this thesis proposal: New Odd and Even Double Factorial Functions as Components Representing the Standard Double Factorial Function.